$$\omega = \frac{2\pi}{T},\qquad v_z = \frac{\Delta z}{T}$$
Ángulo: $$\theta(t)=\omega t + \varphi_0$$
Posición: $$\begin{aligned} x(t) &= x_0 + R\cos\theta(t),\\ y(t) &= y_0 + R\sin\theta(t),\\ z(t) &= z_0 + v_z\,t\,. \end{aligned}$$
Velocidad: $$\begin{aligned} v_x(t) &= -R\,\omega\,\sin\theta(t),\\ v_y(t) &= \phantom{-}R\,\omega\,\cos\theta(t),\\ v_z(t) &= v_z\,. \end{aligned}$$
Aceleración: $$\begin{aligned} a_x(t) &= -R\,\omega^2\,\cos\theta(t),\\ a_y(t) &= -R\,\omega^2\,\sin\theta(t),\\ a_z(t) &= 0\,. \end{aligned}$$